Finite Group Databasebeta

← #17044644

Subgroups — #17044644

Order 4352.

1010 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762772C211yesmaximal, characteristic
2C2×#11762771C211yesmaximal, characteristic
3D17×#407C211yesmaximal, characteristic
4#14528991C211yesmaximal, characteristic, complemented
5#14528990C212yesmaximal, complemented
6#14528989C211yesmaximal, characteristic, complemented
7#14528988C211yesmaximal, characteristic, complemented
8#14528987C212yesmaximal, complemented
9#14528825C212yesmaximal, complemented
10#14528823C212yesmaximal, complemented
11C17×#1855C211yesmaximal, characteristic, complemented
12C23×C4×D17C2211yescharacteristic
13C22×#63223C2211yescharacteristic
14C22×#63218C2212yes—
15C2×M16×D17C2211yescharacteristic
16C2×M16×D17C2211yescharacteristic
17C2×#10587490C2212yescomplemented
18C2×#10587493C2212yescomplemented
19C2×#10587493C2212yescomplemented
20#11762773C2211yescharacteristic
21#11762772—21no—
22#11762772—21no—
23#11762772C2211yescharacteristic
24#11762772C2211yescharacteristic
25#11762772C2212yes—
26#11762772C2212yes—
27#11762771—21no—
28#11762771—21no—
29#11762771C412yes—
30#11762771C412yes—
31#11762771C412yes—
32#11762771C412yes—
33C2×C22⋊#3622C2211yescharacteristic
34C2×#10587491—21no—
35C2×#10587491—21no—
36C2×#10587491C2212yes—
37C22⋊C8×D17—21no—
38C22⋊C8×D17—21no—
39#11762574C2212yescomplemented
40#11762573C2212yescomplemented
41#11762573C2212yescomplemented
42C22×M16×C17C2211yescharacteristic
43C2×C17×#108C2212yescomplemented
44C17×#407C2211yescharacteristic
45C2×C17×C22⋊C8C2211yescharacteristic
46C17×#341C2212yescomplemented
47C24×D17Q811yescharacteristic
48C23×C4×C17C2311yescharacteristic
49C23×Dic17Q811yescharacteristic
50C22×C4×D17—42no—
51C22×C4×D17—42no—
52C22×C4×D17C2×C411yescharacteristic
53C22×C4×D17C2×C411yescharacteristic
54C22×C4×D17C2×C411yescharacteristic
55C22×C4×D17C2×C411yescharacteristic
56C22×C4×D17D411yescharacteristic
57C22×C4×D17D411yescharacteristic
58C22×C4×D17D411yescharacteristic
59C22×C4×D17D411yescharacteristic
60C22×C4×D17Q811yescharacteristic
61C22×C4×D17Q811yescharacteristic
62C22×C4×D17C2311yescharacteristic
63C22×C4×D17C2311yescharacteristic
64C2×M16×C17—21no—
65C2×M16×C17—42no—
66C2×M16×C17C2312yes—
67C2×M16×C17C2311yescharacteristic
68C2×M16×C17C2311yescharacteristic
69C22×C8×C17—21no—
70C22×C8×C17C2312yes—
71C2×#63223—21no—
72C2×#63223—42no—
73C2×#63223C2312yes—
74C2×#63223C2311yescharacteristic
75C2×#63223C2311yescharacteristic
76C22×#3622—21no—
77C22×#3622C2312yes—
78M16×D17—42no—
79M16×D17—42no—
80C2×#63218—21no—
81C2×#63218—21no—
82C2×#63218—42no—
83C2×#63218—42no—
84C2×#63218C2×C414yes—
85C2×#63218C2×C414yes—
86C2×C8×D17—21no—
87C2×C8×D17—21no—
88C17×#108—42no—
89C17×C22⋊C8—21no—
90C17×C22⋊C8—21no—
91C17×C22⋊C8C2×C412yes—
92C17×C22⋊C8C2×C412yes—
93C22⋊#3622—21no—
94C22⋊#3622—21no—
95C22⋊#3622C2×C412yes—
96C22⋊#3622C2×C412yes—
97#10587493—42no—
98#10587493—42no—
99#10587491—21no—
100#10587491—21no—
101#10587491—21no—
102#10587491—21no—
103#10587491—22no—
104#10587491—22no—
105#10587491—22no—
106#10587491—22no—
107#10587491C2×C414yes—
108#10587491C2×C414yes—
109#10587490—42no—
110C24×C17C2×Q811yescharacteristic
111C23×D17—42no—
112C23×D17—42no—
113C23×D17—42no—
114C23×D17C4⋊C411yescharacteristic
115C23×D17C4⋊C411yescharacteristic
116C23×D17C4⋊C411yescharacteristic
117C23×D17C4⋊C411yescharacteristic
118C23×D17C2×Q811yescharacteristic
119C23×D17C2×Q811yescharacteristic
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17C22×C411yescharacteristic
123C22×C4×C17C22×C411yescharacteristic
124C22×C4×C17C2×D411yescharacteristic
125C22×C4×C17C2×D411yescharacteristic
126C22×C4×C17C2×Q811yescharacteristic
127C22×C4×C17C2411yescharacteristic
128C22×Dic17—42no—
129C22×Dic17C4⋊C411yescharacteristic
130C22×Dic17C4⋊C411yescharacteristic
131C22×Dic17C4⋊C411yescharacteristic
132C22×Dic17C4⋊C411yescharacteristic
133C22×Dic17C2×Q811yescharacteristic
134C22×Dic17C2×Q811yescharacteristic
135C2×C4×D17—22no—
136C2×C4×D17—22no—
137C2×C4×D17—22no—
138C2×C4×D17—22no—
139C2×C4×D17—42no—
140C2×C4×D17—42no—
141C2×C4×D17—42no—
142C2×C4×D17—42no—
143C2×C4×D17—41no—
144C2×C4×D17—41no—
145C2×C4×D17—41no—
146C2×C4×D17—41no—
147C2×C4×D17—41no—
148C2×C4×D17—41no—
149C2×C4×D17—41no—
150C2×C4×D17—41no—
151C2×C4×D17—42no—
152C2×C4×D17—42no—
153C2×C4×D17C4⋊C411yescharacteristic
154C2×C4×D17C4⋊C411yescharacteristic
155C2×C4×D17C4⋊C411yescharacteristic
156C2×C4×D17C4⋊C411yescharacteristic
157C2×C4×D17C4⋊C411yescharacteristic
158C2×C4×D17C4⋊C411yescharacteristic
159C2×C4×D17C4⋊C411yescharacteristic
160C2×C4×D17C4⋊C411yescharacteristic
161C2×C4×D17C22×C411yescharacteristic
162C2×C4×D17C22×C411yescharacteristic
163C2×C4×D17C22×C411yescharacteristic
164C2×C4×D17C22×C411yescharacteristic
165C2×C4×D17C2×D411yescharacteristic
166C2×C4×D17C2×D411yescharacteristic
167C2×C4×D17C2×D411yescharacteristic
168C2×C4×D17C2×D411yescharacteristic
169M16×C17—22no—
170M16×C17—22no—
171M16×C17—22no—
172M16×C17—22no—
173M16×C17—42no—
174C2×C8×C17—22no—
175C2×C8×C17—22no—
176C2×C8×C17—22no—
177C2×C8×C17—21no—
178C2×C8×C17—21no—
179C2×C8×C17—42no—
180C2×C8×C17C22×C414yes—
181#63223—22no—
182#63223—22no—
183#63223—22no—
184#63223—22no—
185#63223—42no—
186C2×#3622—22no—
187C2×#3622—22no—
188C2×#3622—22no—
189C2×#3622—21no—
190C2×#3622—21no—
191C2×#3622—42no—
192C2×#3622C22×C414yes—
193#63218—44no—
194#63218—44no—
195#63218—42no—
196#63218—42no—
197C8×D17—42no—
198C8×D17—42no—
199#21949—171nomaximal, Sylow
200C23×C17—22no—
201C23×C17—22no—
202C23×C17—41no—
203C23×C17C2×C4⋊C411yescharacteristic
204C23×C17C2×C4⋊C411yescharacteristic
205C23×C17C22×Q811yescharacteristic
206C22×D17—22no—
207C22×D17—22no—
208C22×D17—22no—
209C22×D17—22no—
210C22×D17—22no—
211C22×D17—22no—
212C22×D17—22no—
213C22×D17—41no—
214C22×D17—41no—
215C22×D17—41no—
216C22×D17—41no—
217C22×D17—41no—
218C22×D17—41no—
219C22×D17—41no—
220C22×D17—41no—
221C22×D17—41no—
222C22×D17—41no—
223C22×D17—41no—
224C22×D17—416no—
225C22×D17C2×C4⋊C411yescharacteristic
226C22×D17C2×C4⋊C411yescharacteristic
227C22×D17C2×C4⋊C411yescharacteristic
228C22×D17C2×C4⋊C411yescharacteristic
229C2×C4×C17—22no—
230C2×C4×C17—22no—
231C2×C4×C17—22no—
232C2×C4×C17—21no—
233C2×C4×C17—21no—
234C2×C4×C17—21no—
235C2×C4×C17—21no—
236C2×C4×C17C2×C4⋊C411yescharacteristic
237C2×C4×C17C2×C4⋊C411yescharacteristic
238C2×C4×C17C23×C411yescharacteristic
239C2×C4×C17C22×D411yescharacteristic
240C2×C4×C17H(5,𝔽2)12yes—
241C2×C4×C17H(5,𝔽2)12yes—
242C2×Dic17—22no—
243C2×Dic17—22no—
244C2×Dic17—41no—
245C2×Dic17—41no—
246C2×Dic17—41no—
247C2×Dic17—41no—
248C2×Dic17C2×C4⋊C411yescharacteristic
249C2×Dic17C2×C4⋊C411yescharacteristic
250C2×Dic17C2×C4⋊C411yescharacteristic
251C2×Dic17C2×C4⋊C411yescharacteristic
252C4×D17—22no—
253C4×D17—22no—
254C4×D17—22no—
255C4×D17—22no—
256C4×D17—21no—
257C4×D17—21no—
258C4×D17—21no—
259C4×D17—21no—
260C4×D17—21no—
261C4×D17—21no—
262C4×D17—21no—
263C4×D17—21no—
264C4×D17—41no—
265C4×D17—41no—
266C4×D17—41no—
267C4×D17—41no—
268C4×D17—41no—
269C4×D17—41no—
270C4×D17—41no—
271C4×D17—41no—
272C8×C17—24no—
273C8×C17—42no—
274C8×C17—41no—
275C8×C17—41no—
276#3622—24no—
277#3622—41no—
278#3622—41no—
279#3622—42no—
280C2×#407—171no—
281C2×#407—171no—
282C2×#407—171no—
283#1855—172no—
284#1855—171no—
285#1855—171no—
286#1855—172no—
287#1855—171no—
288#1855D1711yescharacteristic, complemented
289#1811—172no—
290#1811—172no—
291C22×C17—21no—
292C22×C17—21no—
293C22×C17—21no—
294C22×C17—21no—
295C22×C17—21no—
296C22×C17—21no—
297C22×C17—21no—
298C22×C17—44no—
299C22×C17#43012yes—
300C22×C17C22×C4⋊C411yescharacteristic
301C22×C17#54312yes—
302C2×D17—21no—
303C2×D17—21no—
304C2×D17—21no—
305C2×D17—21no—
306C2×D17—21no—
307C2×D17—21no—
308C2×D17—21no—
309C2×D17—21no—
310C2×D17—21no—
311C2×D17—21no—
312C2×D17—21no—
313C2×D17—44no—
314C2×D17—44no—
315C2×D17—44no—
316C2×D17—44no—
317C2×D17—44no—
318C2×D17—44no—
319C2×D17#43012yes—
320C4×C17—21no—
321C4×C17—21no—
322C4×C17#51812yes—
323C4×C17#53411yescharacteristic
324C4×C17#53411yescharacteristic
325Dic17—21no—
326Dic17—21no—
327Dic17—21no—
328Dic17—21no—
329C24×C4—171no—
330C22×M16—172no—
331C22×M16—171no—
332C22×M16—171no—
333C22×M16—171no—
334C22×M16C2×D1711yescharacteristic
335C2×#108—172no—
336C2×#108—172no—
337C2×#108—172no—
338C2×#108C2×D1712yescomplemented
339#407—172no—
340#407—172no—
341#407—172no—
342#407—172no—
343#407—171no—
344#407—171no—
345#407—171no—
346#407—172no—
347#407—172no—
348#407—341no—
349#407—341no—
350#407—341no—
351#407—341no—
352#407C2×D1711yescharacteristic
353C2×C22⋊C8—171no—
354C2×C22⋊C8—172no—
355C2×C22⋊C8—341no—
356C2×C22⋊C8—341no—
357C2×C22⋊C8—341no—
358C2×C22⋊C8—341no—
359C2×C22⋊C8C2×D1711yescharacteristic
360#341—172no—
361#341—172no—
362#341—172no—
363#341C2×D1712yescomplemented
364C2×C17—22no—
365C2×C17—22no—
366C2×C17—41no—
367C2×C17#231511yescharacteristic
368C2×C17C2×#43011yescharacteristic
369C2×C17C2×#43011yescharacteristic
370D17—22no—
371D17—41no—
372D17—41no—
373D17—41no—
374C25—171no—
375C23×C4—171no—
376C23×C4—171no—
377C23×C4—171no—
378C23×C4—171no—
379C23×C4—171no—
380C23×C4—171no—
381C23×C4—171no—
382C23×C4—171no—
383C23×C4—171no—
384C23×C4—171no—
385C23×C4—171no—
386C23×C4—171no—
387C23×C4—171no—
388C23×C4—682no—
389C23×C4—682no—
390C23×C4C22×D1711yescharacteristic
391C2×M16—21no—
392C2×M16—42no—
393C2×M16—174no—
394C2×M16—174no—
395C2×M16—171no—
396C2×M16—172no—
397C2×M16—171no—
398C2×M16—341no—
399C2×M16—341no—
400C2×M16—341no—
401C2×M16—682no—
402C2×M16—682no—
403C2×M16—682no—
404C2×M16—682no—
405C2×M16—682no—
406C2×M16C22×D1711yescharacteristic
407C2×M16C22×D1711yescharacteristic
408C2×M16C22×D1712yes—
409C22×C8—21no—
410C22×C8—172no—
411C22×C8—341no—
412C22×C8—341no—
413C22×C8—341no—
414C22×C8C22×D1712yes—
415#108—42no—
416#108—682no—
417#108—682no—
418#108—682no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—172no—
422C22⋊C8—172no—
423C22⋊C8—174no—
424C22⋊C8—174no—
425C22⋊C8—341no—
426C22⋊C8—341no—
427C22⋊C8—341no—
428C22⋊C8—341no—
429C22⋊C8—342no—
430C22⋊C8—342no—
431C22⋊C8—342no—
432C22⋊C8—342no—
433C22⋊C8—341no—
434C22⋊C8—341no—
435C22⋊C8C4×D1712yes—
436C22⋊C8C4×D1712yes—
437C17#2194911yescharacteristic, complemented, Sylow
438C24—171no—
439C24—171no—
440C24—171no—
441C24—171no—
442C24—171no—
443C24—171no—
444C24—682no—
445C24—682no—
446C24—682no—
447C24Q8×D1711yescharacteristic
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—171no—
451C22×C4—171no—
452C22×C4—171no—
453C22×C4—171no—
454C22×C4—171no—
455C22×C4—171no—
456C22×C4—171no—
457C22×C4—171no—
458C22×C4—171no—
459C22×C4—171no—
460C22×C4—171no—
461C22×C4—171no—
462C22×C4—171no—
463C22×C4—171no—
464C22×C4—171no—
465C22×C4—171no—
466C22×C4—171no—
467C22×C4—171no—
468C22×C4—171no—
469C22×C4—171no—
470C22×C4—171no—
471C22×C4—171no—
472C22×C4—342no—
473C22×C4—342no—
474C22×C4—342no—
475C22×C4—342no—
476C22×C4—682no—
477C22×C4—682no—
478C22×C4—682no—
479C22×C4—682no—
480C22×C4—681no—
481C22×C4—681no—
482C22×C4—681no—
483C22×C4—681no—
484C22×C4—681no—
485C22×C4—681no—
486C22×C4—681no—
487C22×C4—681no—
488C22×C4—682no—
489C22×C4—682no—
490C22×C4—682no—
491C22×C4C2×C4×D1711yescharacteristic
492C22×C4C2×C4×D1711yescharacteristic
493C22×C4D4×D1711yescharacteristic
494C22×C4D4×D1711yescharacteristic
495C22×C4Q8×D1711yescharacteristic
496C22×C4C23×D1711yescharacteristic
497M16—22no—
498M16—22no—
499M16—22no—
500M16—22no—
501M16—42no—
502M16—342no—
503M16—342no—
504M16—342no—
505M16—342no—
506M16—684no—
507M16—684no—
508M16—682no—
509M16—682no—
510M16—682no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—22no—
516C2×C8—42no—
517C2×C8—174no—
518C2×C8—342no—
519C2×C8—342no—
520C2×C8—341no—
521C2×C8—342no—
522C2×C8—341no—
523C2×C8—682no—
524C2×C8—682no—
525C2×C8—682no—
526C2×C8C2×C4×D1714yes—
527C23—22no—
528C23—22no—
529C23—41no—
530C23—171no—
531C23—171no—
532C23—171no—
533C23—171no—
534C23—342no—
535C23—342no—
536C23—342no—
537C23—342no—
538C23—342no—
539C23—342no—
540C23—342no—
541C23—681no—
542C23—681no—
543C23—681no—
544C23—681no—
545C23—681no—
546C23—681no—
547C23—681no—
548C23—681no—
549C23—681no—
550C23—681no—
551C23—681no—
552C23—6816no—
553C23C4⋊C4×D1711yescharacteristic
554C23C4⋊C4×D1711yescharacteristic
555C23C2×Q8×D1711yescharacteristic
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—171no—
564C2×C4—171no—
565C2×C4—171no—
566C2×C4—171no—
567C2×C4—342no—
568C2×C4—342no—
569C2×C4—342no—
570C2×C4—342no—
571C2×C4—342no—
572C2×C4—342no—
573C2×C4—341no—
574C2×C4—341no—
575C2×C4—341no—
576C2×C4—341no—
577C2×C4—341no—
578C2×C4—341no—
579C2×C4—341no—
580C2×C4—341no—
581C2×C4—681no—
582C2×C4—681no—
583C2×C4—681no—
584C2×C4—681no—
585C2×C4—681no—
586C2×C4—681no—
587C2×C4—681no—
588C2×C4—681no—
589C2×C4—681no—
590C2×C4—681no—
591C2×C4—681no—
592C2×C4—681no—
593C2×C4C4⋊C4×D1711yescharacteristic
594C2×C4C4⋊C4×D1711yescharacteristic
595C2×C4C22×C4×D1711yescharacteristic
596C2×C4C2×D4×D1711yescharacteristic
597C2×C4#1058769112yes—
598C2×C4#1058769612yes—
599C8—24no—
600C8—42no—
601C8—41no—
602C8—41no—
603C8—344no—
604C8—681no—
605C8—681no—
606C8—682no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—44no—
615C22—172no—
616C22—341no—
617C22—341no—
618C22—341no—
619C22—341no—
620C22—341no—
621C22—341no—
622C22—341no—
623C22—341no—
624C22—341no—
625C22—341no—
626C22—341no—
627C22—684no—
628C22—684no—
629C22—684no—
630C22—684no—
631C22—684no—
632C22—684no—
633C22#1176285612yes—
634C22C2×C4⋊C4×D1711yescharacteristic
635C22#1176343412yes—
636C4—21no—
637C4—21no—
638C4—341no—
639C4—341no—
640C4—341no—
641C4—341no—
642C4#1176328112yes—
643C4#1176336911yescharacteristic
644C4#1176337011yescharacteristic
645C2—22no—
646C2—22no—
647C2—41no—
648C2—342no—
649C2—681no—
650C2—681no—
651C2—681no—
652C2#1453139511yescharacteristic
653C2D17×#43011yescharacteristic
654C2C2×#1176285611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1855C2
socleC22×C17C22×C4⋊C4
prime radicalC24×D17Q8
cosocleC22×C4×C17C24
hypercenter#1855D17
hypocenterC17#21949
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1855

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #14528991C2semidirect
5. #14528990C2semidirect
6. #14528989C2semidirect
7. #14528988C2semidirect
8. #14528987C2semidirect
9. #14528825C2semidirect
10. #14528823C2semidirect
11. C17×#1855C2semidirect
17. C2×#10587490C22semidirect
18. C2×#10587493C22semidirect
19. C2×#10587493C22semidirect
39. #11762574C22semidirect
40. #11762573C22semidirect
41. #11762573C22semidirect
43. C2×C17×#108C22semidirect
46. C17×#341C22semidirect
288. #1855D17semidirect
338. C2×#108C2×D17semidirect
363. #341C2×D17semidirect
437. C17#21949semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117627722
C2×#117627712
D17×#4072
#145289912
#145289902
#145289892
#145289882
#145289872
#145288252
#145288232
C17×#18552
#2194917